So, I read somewhere that I'll lose fat by cutting dairy out of my diet. Should I do this?

Is this a good thing for a MMA diet

You see, I'm around 5'6 and weight 145.5 which is a little to much to fight feather weigth, I wanna go down to around 138-140 but I wanna do this by losing fat. Is this something I should do? Or do you recommend something else?